When attempting to turn on LinkedIn’s two-step verification account security feature, some users may discover that clicking the “Turn on” button does not do anything. No text message is sent and it is as if the button is not associated with a command – nothing happens.
In this situation, try selecting “Go to previous version of Settings” at the bottom:
This should bring up the LinkedIn Settings screen in a former style. Select “Account” on the left and the menu should include “Manage security settings” as an option. Click on that and you should be able to turn on two-step verification:
This error is likely due to incompatibility between the browser and LinkedIn.